Frequency selective circuits



H.. ELsAssER FREQUENCE' SELEG'IIVE C I RCUI T S Filed August 13,. 1920 3 Sheets-Sheet l ATTORNEY Jan. 5,-19'26.

1,568,143 H. w. ELsAssER FREQUENCY SELECTIVE CIRCUITS Filed August 13, 1920 s Sheets-Sheet 2 ATTORNEY Jan. 5, 192e. 1,568,143

' H. W. ELSASSER FREQUENCY SELECTIVE CIRCUITS Filed August 13,. 1.920 3 Sheets-Sheet 5 INVENTOR f/,w ATTORNEY a citizen of the United States, residing at Patented Jan. 5, 1926.

UNITED STATES '1 ..TENroFFlcE.-

my w. ans-Assas., ois* NEW Yonx, N.' Y., assrenon 'ro marcar 'rumori an 'rameaux COMPANY, a conrona'rIoN or Naw Your.

renommer snLnc'rIvn cmcurrs.

Application illed August 13, 1920. Serial No. 403,809.

To all whom t may concern.' Be it known that I, HENRY W. ELsAs'snn,

New York, in the county .of New /York and State of New York, have invented certain Improvements in -Frequency Selective Circuits, of which'the following is a specification.

tive circuits.

It contemplates a network of impedances having a period of series resonance Vand a period of parallel resonance, so that its imance for a certain frequency of current 1s very low and for another, very high.

The invention proposes, further the use of a network of this character in combination with other impedance elements in a eriodic structure of the type illustrated and escribed in the patents to G. A. Campbell, 1,227,113v and 1,227,114 of May 22, 1917. Certain new and useful types of wave filters are thus arrived at, the characteristics of which are explained hereinbelow.

This application is related to certain copending cases, Serial Numbers 403,367, 403,- 368, 403,370, filed of even date herewith.

A good understanding of the invention may now -be had from the following description of certainspecic embodiments thereof, having reference to the accompanying drawin which,

i 1 is a diagrammatic view showing one orm of network embodying the. invention;

Figs 2 to 5 inclusive aredi atic vlews showing -various types of ters comprising the network of Fig. 1;

Fig. 1^ is a graph showing thevariation with f work of ig. 1., and

Figs. 2^ to 5^ inclusive, are graphs showing the variation in attenuation of the filters of Figs. '2 to 5, respectively.

- Similar characters ofreference designate similar parts in each of the several views.

The network ofFig. '1 consists of a condenser C, in parallel with an inductance L, and a condenser C2 which are in series with each other and thus constitute a series res- This invention relates to frequency-sehec-- uency in the impedance of the. netonant path. The impedance of the condenser Cl isl A v -2'1rf, eing the frequency of the current. The impedance of the series resonant path is iwLz-,' hence the impedance value ofthe entire netswork i`s` fwfh+^1 f Z :M (1) iwL.+ 1 +.1

m m Place for convenience ff (2)v lwhere f, is the frequency at which Lz and IC, n re resonant. Substitute equation 2 inequat1on 1 and simplify. Then The expression in the brackets of the above equation may be placed equal to K. Then Z-MLK (4) where .y

impedance of the network changes with frequency as may be seen by an ins ection of equation 4. At low frequencies, t e impedance of the network is negative, but as the frequency is raised, the impedance changes to positive, the point of crossing of the axis of abscissae denoting seriesresonance of the path containing C2 and L2, or zero impedance of the network. The impedance then increases until, at the frequency at which the elements of the network are in parallel resonance, its value is infinite. The impedance then changes sign and thereafter decreases, approaching zero at infinite frequency. The network therefore, has two periods of resonance, a period of series resonance at one frequency and a period of parallel resonance at a higher frequency. The period of series resonance depends on the relative value of only two impedance elements, namely L2 and C2, and the period of parallel resonance is governed by the values of all three reactances. The curves of Fig. 1A are drawn for an ideal network containing no resistance or other dissipative elements, but in anactual case, the resistance may be made so small that its effect is practically negligible. `It thus appears that y the network of Fig. l may be used as a selective circuit-for passing current of series resonant frequency and preventing the passage of current of parallel resonant frequency.

I have found, moreover, that by employ ing the network as a shunt and series impedance in a periodic structure like that disclosed in the Campbell patents hereinbefore mentioned, certain new typesV of wave fil` Vters are arrived at, which filters have certain new and valuable characteristics which I shall now describe.

Figs. 2, 3, 4, and 5 illustrate four types of filters employing the network of Fig. 1,

the former two of these views showing thenetwork as a shunt impedance element and the latter two, as a series impedance element of the filter section. Figs. 2 ,and 3 show an inductive and a capacity reactance respectively as the series lmpedanceelement, and Figs. 4 and 5 show thesame reactances respectively as the shunt impedance elements.

`'lhe properties of the above filters may be determined from certain mathematical expressions which set forth the relations existing between the frequency of. current and the impedance elements of the filters.

In the Campbell patents hereinbefore mentioned, it was shown (equation 2) that for a periodic structure of the type now under consideration, in which the series impedance per section is Z,l and the shunt impedance per section is Z2, the attenuation per section of the filter may be derived from the relation cosh /`=l+l (6) in which denotes the propagation constant of the structure. The variation of the attenuation of any filter with frequency of current may, therefore, be deduced from equation 6, whenl the corres ndin values of Z1 and Z2 are substitute therein. For the filter shown in Fig. 2, the value of Z1 is Z, y'wL (7) and according to equation 4 above),

Z2 j'wrLzK (8) 'fl`he resultant equation for cosh is, thereore,

Fig. 2A is a graph vshowing the variation of the attenuation of the filter of Fig. 2, as computed from equation 9. The axis of the abscissze is laid off in ratios of f to f, and the axis of the ordinates in values of the attenuation constant per filter section. An inspection of the curves shows that the attenuation is nil for two ranges of frequencies, 0 to f, and f, to f4. The filter, in other words, passes without attenuation, the two ranges of frequencies. The lter is, therefore, a combined low-pass and band filter and performs the functions of both. It is characterized, moreover, by having infinitezattenuation at a frequency, fm which is close to f2, and it discriminate's, consequently, with particular sharpness against frequencies ,just above the upper limit of the low-pass range.

The frequencies f2, f, and f, may be evaluated as follows. It was shown in the said Campbell patents, that for unattenuated transmission must be a pure imaginary, and that, therefore, the value of cosh must lie between :l: 1. Thefrequencies which limit the ranges of free transmission may consequently be determined by placing equation 9 equal to +1 and -1 respectively, and solvingfor f. lfVhen this is done, it will be found that the roots are respectively,

:i C1+z f 2^/ (Il) l 1 L00; '1100i 1 1 )2 hvsa/hoff uefa+4 wao. 12)

The frequency fm at which the attenuation 1 C +C is infinite, may beevaluated by placing equa- .fh :5; l CCzL (16) tion 9 equal to and solving for f, whence l fm (13) The attenuation characteristics of the remaining filters may be arrived at in a similar manner. The curves of Fig. 3^ show stantial attenuation only a Single band, the limiting values of which are f1 and fi.. The filter is further characterized by having'infinite attenuation per section at a frequency fm below l. This frequency may be chosen within y t e lower attenuated range, but preferably so as to lie close to f1, so that the filter has a' sharp cut-off at the lower limit 'of the transmitted band.

The frequencies fl', fh, and fm may be evaluated similarly as the limiting frequencies of the filter of Fig. 2. The expression for cosh in the present case is, since Z1 is a capacity reactance,

+7- 1 w00 cosh -m44 Placing equation 14 equal res ectiv'ely to +1 and 1, and solving for f, t e roots will be found to be that the filter of Fig. 3 passes without Sub- When equation 14 is placed equal to and solved for f, the frequency of attenuation, fm, is found to be 1 fm 21m/MC2 (17) The curves of Fig. 4^ show that the filter of Fig. 4 is'similar to that of Fig. 2 in that it has two ranges of free transmission. It differs therefrom, however, in that it passes all frequencies Vabove a certain value without substantial attenuation, and serves consequently as a combined band and high-pass filter. The frequency fm, at which the atn tenuation is infinite, may be so chosen as to lie close to f3, thus giving the lter a sharp cut-off at the lower limit of the high-pass band.' VThese curves have been derived from the expression,

l jwrLzK 2 jwLo L00." not y enc.

MC1 LlCz Lo 2 +4E+1 1 6 (19) LoCi E@ (21) The 'curves of Fig. 5A show that the filter of Fig. 5 is of the single band type and similar to that of Fig. 3, differing therefrom,

however, in that the frequency of infinite attenuation lies inl the upper attenuated range. This filter, therefore, may be caused to have a sharp cut-off at the upper limit of the band. The attenuation curve of Fig. 5A is derived from the expression,

cosh /"=-7w;f+1 (23) luf-C0 and the values of f1 and fh and fm are ob? tained by placing the above expression for cosh equal to +1, -1 and respectively.

It should be noted that the attenuation curves herein illustrated refer to the ideal structure in which the resistance 0f the inipedance units is zero. In a practical filter there is a departure from these curves, ow-

ing to energy dissipation. In anycase, however, the resistance may be made so small `that the departure from the ideal is praclining the rang-es of 4free transmission. This leaves one condition open to choice, and this may be taken as the impedance ofthe filter at any desired frequency, or as the value of anyone of theelements of the filter section. In the kdesign of a filte:` of the type of Fig. 3, two of the design conditions may be chosen as the frequencies fl, and fh, and the third as fm, thus leaving the fourth to be chosen in accordance with any other condition that mayprevail. Similar considerations apply to the remaining types of filters.

As an example of the application of the formulae, let it be required to design a filter of the type illustrated in Fig. 5, which shall transmit frequencies between 400 and 2500 cycles, and which shall have maximum, ideally infinite, attenuation at 2750 cycles, so that it has a particularly sharp cut-off at the upper limit of the freely transmitted range. Frequencies f1, fh and fm are thus specified as 400, 2500 and 2750 cycles respectively. As a fourth design factor, let it be assumed that certain .considerations dictate that the value of C2 shall be 3.00

microfarads. Applying formula 24 We find that 1 400= an/axlo-L2 hence' L2=.0528 henries Substituting in (26) We have 1 2750 I 2f C1 3 1o -o528 Hence 0,:.0649 microfarads Finally according to (25) Therefore 00:.0559 microfarads All the constants of the filter are thus determined. It AWill readily be seen that, inl1 stead ofthe above-mentioned set of conditions, any others involving the filter impedances may be imposed, it being understood that the above example is merely a simple illustration, and in no Way limits the invention.

Although only certain forms of filters embodying the invention are shown and described herein, itis easily understood that various changes and modifications may be made therein Within the scope of the. followin claims, Without departing from the spirit and scope of the invention.

While it is assumed, for the purpose of computation, that the impedance elements of a filter are pure reactances, it is, of course, understood that these reactances, in the forms ofcoils or condensers, must inevitably ave a little resistance. In this respect the procedure is no different from that in other applications of mathematics to engineering. Ina problem in dynamics, friction may be neglected. In problems in Statics, strains are often neglected. Similarly, in this case, for the purposes of computation, the resistance of the coils and condensers is neglected.

The unavoidable resistance is greater in a.

coil than in a condenser. Hence, for some purposes, a filter which has 1ts reactance ele- .ments principally inthe form of condensers instead of coils, will involve less departure from theory. e

Referring to the drawings of the present ment in each section Vdensers,

case, it will be seen that in Figs. 3 and 5 each filter section is made up of three condensersand only one coil. These lters will have the advantage just pointed lout.

What is claimed is: v

1. A wave filter ofthe type having similar recurrent sections, each section having a series element anda shunt element, one of those elements in each section consisting of a single lumped reactance andthe other elebeing a network comprising a capacity' reactance in parallel with a path comprising van inductive reactance and a capacity reactance in series with each other. 2. A filter for an electric circuit, consisting of a plurality of recurrent sections, each such section comprising an `impedance in series with the circuit and an impedance in shunt thereto, one of said impedances consisting of .a single reactance element andthe other, of. a network ,comprising a ycapacity reactance in parallel with a path comprising with. an induca capacity reactance in series tive reactance.

3. A wave filter of periodic structure comprising sections each having four and only four reactances of which three are embodied in condensers and one in a coil, said three condensers constituting three different capacities adapted to function in different phases.

4. A single band filter with recurrent sec- -ti'ons having a frequency of maximum attenuation close to one side of the band whereby the filter will have a sharp cut-off at that side of the band and having only one coil per section, the remaining impedance elements of the sections being conthe said coil and one of the '.said condensers in combination being resonant at the said frequency of maximum attenuation.

5. A wave filter having recurrent sections with four reactance elements in each section and having a single transmission band, said four reactances being determine-d as functionsof (l) one limiting frequency, (2) the other limiting frequency, (3) the frequency for maximum attenuation close to one o said limiting frequencies outside the transmission range and (4) ythe mid-frequency characteristic impedance of the filter within the transmission range.

6. A wave filter of the type having recurrent sections, each section consisting of a series impedance and a shunt im a network consisting of three reactance elements, and the other such impedance Aconsisting of only a single reactance element, sai filter having a single continuous free transmitting range between finite limiting frequencies and infinite attenuation at a frequency outside that range.

f 7. A wave filter of the type having recurrent sections, each section consisting of a series impedance and a shunt impedance, one of these impedances being a simple capacity reactance, the other such impedance being embodied in a three-element network, the filter having a single free transmitting` range between ytwo finite frequencies and having infinite attenuation at a frequency outside that range.

8The method of discriminating among various alternating current frequency components from zerofrequency up to a high frequency, which consists in attenuating the components from zero up to a certain finite limiting frequency with a maximum of attenuation at a frequency only a little less than this finite limit, then passin currents from this finite limit up to .a hig ier limiting frequency and then attenuating all currents higher than this last mentioned limiting frequency.

k 9. The method of discriminating among a' plurality of alternating current components of various frequencies, which consists in attenuating all components of frequency from zero to a certain finite limiting frequency, then passing all components from thisl frequency to a certain higher finite dance, v -one of these impedances being ma e up of doo limitingfrequency and then attenuating all components above said last mentioned frequency with a maximum of attenuation close to one of said two limiting frequencies.

In testimony whereof, I have signed my naine to this specificationthis 10th day of f August 1920.

HNRY W. ELSASSER. 

